What is the distance between #(3, –1, 1) # and #(–3, 2, –3) #?

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Answer 1 · 2018-03-27T23:05:54

See a solution process below:

The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(-3) - color(blue)(3))^2 + (color(red)(2) - color(blue)(-1))^2 + (color(red)(-3) - color(blue)(1))^2)#

#d = sqrt((color(red)(-3) - color(blue)(3))^2 + (color(red)(2) + color(blue)(1))^2 + (color(red)(-3) - color(blue)(1))^2)#

#d = sqrt((-6)^2 + (3)^2 + (-4)^2)#

#d = sqrt(36 + 9 + 16)#

#d = sqrt(45 + 16)#

#d = sqrt(61)#

Or

#d ~~ 7.81#